+0  
 
0
64
1
avatar

What is the value of the leading coefficient a, if the polynomial function P(x) = a(x + b)2(x − c) has a multiplicity of 2 at the point (−1, 0) and also passes through the points (7, 0) and (0, −14)?

 

A:2

B:-2

C:7

D:-14

 

Thanks for the help :)

Guest Mar 13, 2018
Sort: 

1+0 Answers

 #1
avatar+86604 
+1

If we have a multiplicity of 2 at  (-1,0)  and the point (7,0) is also on the graph, we must have that

 

P(x) =

a (x + 1)^2 (x - 7)      

a (x^2 + 2x + 1) (x - 7)  

a(x^3 + 2x^2 + x -7x^2 -14x - 7)  

a(x^3 - 5x^2 - 13x - 7)  

 

And if   (0, -14)  is on the graph.....we have that

 

-14  = a ( 0^3 - 5(0)^2 - 13(0)  - 7)

-14 = -7a

a  = 2

 

Here's a graph : https://www.desmos.com/calculator/wbejrdzi2x

 

 

 

 

cool cool cool

CPhill  Mar 13, 2018

24 Online Users

avatar
avatar
avatar
New Privacy Policy (May 2018)
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  Privacy Policy